Monday, January 2, 2012

Randomness of the d20

The d20 has got to be the most fickle die out there, how many times have monsters rolled multiple 20s and the players rolled 2s and 3s. Variation in the dice is what makes the game fun, but too much variation can be problematic. Thus I'm going to be writing up some rules for using 2d10 rather than 1d20. Effectively, the d20 has an equal 5% chance to roll any number on the die, multiple rolls result in a curve. With 2d10, there is a curve, there's only 1% chance to roll 2 1s or 2 10s. the mean roll will be 11, with a full 10% chance to roll 11, 28% chance to roll 10-12, 40% chance to roll from 9-13, and 54% chance to roll in the 8-14 range. This provides a beautiful pyramid shaped curve, not a bell curve which can be obtained with 3 dice, but better than a straight 5% across the board.  This system creates a game which is easier to judge the difficulty of skill checks, the likely hood that someone will fail a DC5 climb check which should be a simple check changes from 20% to 6%; possible but not as likely.  Using this system obviously a 1 wouldn't be an automatic failure, double ones would be. a 1% chance, with 1% chance, I see no problem with using a fumble system. Critical successes are reduced in chance because they are much less likely, so crit weapons such as a rapier, have a 6% chance to cause a crit threat, however, improved crit  on an 18+ weapon poses a problem in that it has a 21% chance to cause a threat, this is a major difference, though less than the current 30% chance it's 21x more likely than a base 20 weapon in this system. so I need to figure this out. This will be one of my design considerations.

chance of rolling...
2 1% = 1%
3 2% = 3%
4 3% = 6%
5 4% =  10%
6 5% =  15%
7 6% =  21%
8 7% =  28% 
9 8% =  36%
10 9%  =  45%
11 10%  =  55%
12 9%  =  45%
13 8%  =  36%
14 7%  =  28%
15 6%  =  21%
16 5%  =  15%
17 4%  =  10%
18 3% =  6%
19 2%  =  3%
20 1%  =  1%